# Model theory without tears?

Ah well, you win some and you lose some. I was writing for months about recursive ordinals and proof theory with a view to a short-ish book. And now, quite a way in, I realise that I have to go back to the drawing board, do a lot more thinking and reading if I am to have anything both interesting and true to say, and then (maybe) start over. Well, at least being retired I don’t have ‘research productivity’ (or whatever it is currently called) to worry about. Frustrating, though.

As a distraction, initially just with a view to updating one of the less convincing parts of the Teach Yourself Logic Guide in the next version, I’ve been looking again at some of the available treatments of elementary model theory. One immediate upshot is that there are new pages (briefly) on Jane Bridge’s Beginning Model Theory and (rather more substantially) on María Manzano’s Model Theory linked along with some other recent additions at the Book Notes page.

Now, the books by Bridge and Manzano have their virtues, of course, as do some other accounts at the same kind of level, But still, the more I read, the more tempted I am to put my hand to trying to write my own Beginning Model Theory (or maybe that should be a Model Theory Without Tears to put alongside Gödel Without Tears). The exegetical space between a basic treatment of first-order logic and the rather sophisticated delights of (say) Wilfrid Hodges’s Shorter Model Theory and David Marker’s Model Theory isn’t exactly crowded with good texts, and it would be fun to have a crack at. And unlike the recursive ordinals project, at least I think I understand what needs to be said! Which is a good start …

### 3 thoughts on “Model theory without tears?”

1. If I may leave a suggestion, it’d be interesting to see a more philosophical treatment of quantifiers (such as the discussion found in Goldfarb’s “Logic in the twenties”). It’s generally said that one of the single most important innovations of the current logical calculus is the invention of the quantifier, specially when coupled to polyadic quantification; however, it seems to me that, more often than not, this slogan is not adequately explained. Since most logical books which go reasonably in depth about the relevant material (e.g. Skolem functions) are not very philosophical (nothing wrong with that!), perhaps this would be a good opportunity to write something a bit more substantial about this.

2. It sounds like you may at least have learned something about the obstacles, obscurities, and pitfalls along the path to understanding recursive ordinals and proof theory, and that can be interesting in itself.

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